The sudoku
These are the 21 clues. The rules are the usual ones: 1 to 9 in every row, every column and every three-by-three box, with no repeats.
If you are going to try it, copy it onto paper with plenty of room for notes. You will need it.
Where it comes from
It was published in 2012 by Arto Inkala, a Finnish mathematician who had spent years making hard sudokus on purpose. Newspapers ran it as “the world's hardest sudoku”, and one went as far as rating it an 11 on a scale of 1 to 5. It is known as the Everest.
It was not Inkala's first: in 2006 he had published AI Escargot, which held the same reputation for years.
Why it is so hard
It is not the small number of clues. The minimum for a sudoku to have a single solution is 17, and some 17-clue sudokus take no time at all. What counts is the reasoning it demands, not how empty it looks.
There is nowhere to start. If you note in every square the digits that could go there, you get more than four on average, and only one square has two.
The usual techniques do not work. Not the naked single, not the hidden single, not pairs, not the X-Wing, not chains: none of them places a single digit.
How sudoku difficulty is measured
There is no official measure. The one enthusiasts use is the hardest technique a puzzle requires: an easy sudoku falls by spotting which square allows only one digit, an expert one needs chains of several steps, and beyond that there are a handful that give in to no technique at all.
Some programs score every sudoku this way, and on their lists the Everest is near the top, next to others with names of their own:
- Inkala, 2006 AI Escargot
- Inkala, 2012 Everest
- Sudoku forums Golden Nugget
- Sudoku forums Platinum Blonde
Which of them is the hardest depends on who you ask.
How to attempt it
Note every candidate. In each empty square, the digits that are not already in its row, its column or its box. It takes a while, but without it there is nothing to look at.
Start with the square that has two. It is the one in row 8, column 7: only 3 and 9 fit there.
Assume one and keep going. Put in the 3, say, noted separately, and work out everything that follows from it. Sooner or later two equal digits will clash in a row, a column or a box, or a square will be left with none.
If it clashes, it was the other one. Rub out what you deduced from the assumption and put in the 9. What follows is now certain, and further on you may have to assume again.
Experts solve it with very long chains (“if a 3 goes here, then over there…”), which comes to the same thing: assume and keep going until something does not add up.
The solution
Show the solution
Hard sudokus you can solve by reasoning
If you like the challenge but not the guessing, every one of these can be solved with logic, step by step.
Hard sudoku, free: in your browser, with a hint that explains the next step if you get stuck.
Expert sudoku, free: the ones that call for X-Wings and chains, the step just below the Everest.
Printable: PDF booklets of ten sudokus per level, with the solutions at the back.
If you like mysteries: Sudoku Detective, a sudoku without numbers where you place suspects and unmask the murderer.
Frequently Asked Questions
What is the world's hardest sudoku?
The best known is the Everest, published by Arto Inkala in 2012. There is no official measure, and others share the reputation, such as AI Escargot (also by Inkala), Golden Nugget and Platinum Blonde.
How many clues does the world's hardest sudoku have?
The Everest has 21. But difficulty does not depend on how many clues there are: some sudokus with 17, the lowest possible, are easy.
Does it have a single solution?
Yes. There is only one way to complete it, and it is at the end of this article.
Can it be solved without guessing?
With the usual techniques not a single digit can be placed. You have to assume a digit and follow it until it clashes, or use very long chains that, at heart, do the same.
What is the minimum number of clues in a sudoku?
17. It has been proved that no sudoku with 16 clues has a single solution.
Where can I play hard sudokus for free?
At sudokudetective.com, in five levels from very easy to expert, with no sign-up, and also as printable PDFs.
Pass it on to a friend